Space of modular forms of level 216, weight 2, and Character 216.d

• Label: 216.2.d
• Level: $216$
• Weight: $2$
• Character orbit: 216.d
• Rep. character: $\chi_{216}(109,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $72$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(72\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(216, [\chi])\).

	Total	New	Old
Modular forms	42	16	26
Cusp forms	30	16	14
Eisenstein series	12	0	12

Trace form

\( 16 q + 2 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
216.2.d.a	$216$	$2$	216.d	8.b	$2$	$4$	$4$	$1.725$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-6}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{8}^{2}q^{2}-2q^{4}+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
216.2.d.b	$216$	$2$	216.d	8.b	$2$	$4$	$4$	$1.725$	\(\Q(i, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+q^{7}+\cdots\)
216.2.d.c	$216$	$2$	216.d	8.b	$2$	$8$	$8$	$1.725$	8.0.629407744.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(216, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(216, [\chi]) \cong \)